1. Let X1, Xn be i.i.d. random variables with a pdf .... f(x) = = e-(x-0), 10, x > 0, elsewhere for a constant parameter 0. This pdf is called the shifted exponential. (a) Compute the c.d.f. of Y = min(X1, ..., Xn). and investigate the distribution that Yn converges in distribution. (b) Compute the c.d.f. of Zn = n(Y₁-0). Investigate the distribution that Zn converges in distribution.

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A: K=? V(X)=?

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Q: 3. Suppose that X is a continuous random variable with pdf 32², 0<x< 1 0, otherwise Let Y= 2X + 3.…

A: f(x)=3x2; 0&lt;x&lt;1

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A:

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A: Given: The cumulative distribution function is as follows F(x) = x3     0&lt; x &lt; 1

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Q: None

A: Step 1:Step 2:Step 3:Step 4:Option(E) : correct

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A: Here X~ Poi(k). Then, P(X=x)=e-kkxx!,x=0,1,2,...0,otherwise a.)The Moment Generating Function of X…

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A: Here we need to find the second moment and the variance.

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A: In

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A: Here, Beta(2,3) F(x) = 6x^2 - 8x^3 + 3x^4

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Q: 5. Let X and Y be independent random variables such that X - exp(A) and Y ~ exp(). (a) What is the…

A: It is an important part of statistics. It is widely used.

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A: y1 0.04304550 y2 0.50263474 f(x)=θe-θx ; x≥0 1) Read the data into R x&lt;- c(0.04304550,…

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A: The pdf is given as follows:f(x) = { (1/6)e^(1/6x) ; x &gt; 0

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A: Please see the next step for solution.

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A: The pdf of X is

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A: In this problem, we are considering the likelihood ratio () in the context of statistical hypothesis…